A circuit structure designed to implement a Hilbert transform has a time-continuous FIR (Finite Impulse Response) filter for its basic component, as readily understood by one skilled in the art. More particularly, a Hilbert transform is essentially a constant module 90° phase shifter. This characteristic can be implemented by an impulsive response FIR filter as illustrated in FIG. 5, for example. The frequency response of such a FIR filter can better approach an ideal response by increasing the filter length. The accompanying FIG. 1 shows schematically a conventional FIR filter which includes a plurality of delay cells cascade connected together between an input terminal and an output terminal.
A distinguishing feature of the cells is that they carry the same amount of time delay, designated Td. The signal output from each cell is then multiplied by a predetermined coefficient c0, . . . ,cn. The summation of all the signals, each multiplied by a respective one of the coefficients c0, . . . ,cn gives a value Y representing the impulse response of the filter.
The performance of a time-continuous FIR filter is also linked to another parameter, that is, the bandwidth of the signal being input to the chain of the delay cells. The greater the bandwidth, the larger becomes the number of the FIR filter coefficients required for a closer approach to the ideal Hilbert transform.
It is a recognized fact that the frequency response of an amplified signal amplitude is related to the frequency response of the signal phase. As the input signal bandwidth grows wider, the phase frequency response becomes smaller, and the so-called group delay is reduced. In fact, the group delay is the derivative of the phase with respect to frequency.
In other words, with an input signal having a broad bandwidth, a FIR filter with a very large number of coefficients must be used to obtain a desired frequency response. However, this requires fairly complicated and expensive circuit structures, and a demanding one in terms of circuit area.
Furthermore, where the input signal has different spectrum forms, there are no circuit structures available which can handle the frequency response in an optimum manner. It is customary in such cases to adopt either of two different approaches.
A first approach employs a FIR filter which has a fixed number of coefficients c0, . . . ,cn so that the filter performances are those as desired for all the spectrum inputs. A second approach uses a filter having coefficients c0, . . . ,cn which can be programmed to fit the spectrum of the input signal.
The first approach obviously involves a larger number of elements than the second approach. However, the basic element in the first approach is that it is simpler to construct on account of the coefficients being non-programmable. While being advantageous from several aspects and substantially meeting current requirements, neither the first nor the second of the above approaches fill all the demands of processing input signals whose spectrum is unknown a priori.